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Calculus of Variations with Classical and Fractional Derivatives

Odzijewicz, Tatiana;  Torres, Delfim F. M. — 2012

Mathematica Balkanica New Series

MSC 2010: 49K05, 26A33 We give a proper fractional extension of the classical calculus of variations. Necessary optimality conditions of Euler-Lagrange type for variational problems containing both classical and fractional derivatives are proved. The fundamental problem of the calculus of variations with mixed integer and fractional order derivatives as well as isoperimetric problems are considered.

A remark on local fractional calculus and ordinary derivatives

Ricardo Almeida;  Małgorzata Guzowska;  Tatiana Odzijewicz — 2016

Open Mathematics

In this short note we present a new general definition of local fractional derivative, that depends on an unknown kernel. For some appropriate choices of the kernel we obtain some known cases. We establish a relation between this new concept and ordinary differentiation. Using such formula, most of the fundamental properties of the fractional derivative can be derived directly.

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